Circular Disformal Kerr: An Exact Rotating Black Hole Beyond GR

Abstract: The Kerr solution is the cornerstone of General Relativity (GR) for modelling astrophysical rotating black holes and for testing GR through gravitational-wave observations and black hole imaging. Understanding how the Kerr geometry is modified in alternative theories of gravity is therefore a crucial step toward constraining possible deviations from GR. Despite their importance, exact analytical solutions describing rotating black holes in modified gravity are rare, limiting our ability to explore novel phenomenology and to design robust observational tests of new physics. In this work, we present a new exact rotating black hole solution within a specific scalar-tensor theory belonging to the Horndeski class. The solution is obtained via a disformal transformation acting on a Kerr stealth black hole. Crucially, unlike previous constructions, the disformal transformation of our chosen seed configuration preserves circularity, ensuring that many of the geometrical and physical properties that make the Kerr spacetime so compelling are retained. We refer to the resulting geometry as the Circular Disformal Kerr solution. Remarkably, key features such as the structure of Killing horizons, the ergosphere, and the absence of causality violations closely mirror those of the Kerr metric. The spacetime is algebraically general, corresponding to Petrov type I. This new exact solution therefore provides a rare example of a rotating black hole beyond GR that closely mimics the Kerr geometry, offering a valuable theoretical laboratory to investigate the phenomenology of Kerr-like black holes in modified gravity.